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arXiv · 1412.5747

Boundary $\varepsilon$-regularity in optimal transportation

Shibing Chen·Alessio Figalli
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Abstract

We develop an $\e$-regularity theory at the boundary for a general class of Monge-Amp\`ere type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between H\"older densities supported on $C^2$ uniformly convex domains are $C^{1,\alpha}$ up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost $-x\cdot y$.

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Shibing Chen, Alessio Figalli. 2014-12-18. Boundary $\varepsilon$-regularity in optimal transportation. https://arxiv.org/abs/1412.5747

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